In this study, an exact Dynamic Programming formulation is developed for price based revenue management in the airline industry. Structural properties of the optimal pricing policy are presented first. Then, the optimal policy is investigated for four different price-demand relationships and the characteristic properties of the airline demand are discussed. Performance of the proposed Dynamic Programming formulation is numerically compared with an alternative approximate approach based on the repeated use of a Mixed Integer Programming model and also with intuitive methods of temporal price discrimination. The numerical results show that significant revenue improvements are obtained by the proposed dynamic pricing methodology. (C) 2019 Elsevier Inc. All rights reserved.